{"id":"https://openalex.org/W4307407384","doi":"https://doi.org/10.1088/1402-4896/ac9dc6","title":"A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems","display_name":"A wavelet-based collocation technique to find the discontinuous heat source in inverse heat conduction problems","publication_year":2022,"publication_date":"2022-10-27","ids":{"openalex":"https://openalex.org/W4307407384","doi":"https://doi.org/10.1088/1402-4896/ac9dc6"},"language":"en","primary_location":{"id":"doi:10.1088/1402-4896/ac9dc6","doi":"https://doi.org/10.1088/1402-4896/ac9dc6","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1402-4896/ac9dc6","pdf_url":"https://iopscience.iop.org/article/10.1088/1402-4896/ac9dc6/pdf","source":{"id":"https://openalex.org/S59012888","display_name":"Physica Scripta","issn_l":"0031-8949","issn":["0031-8949","1402-4896"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physica Scripta","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://iopscience.iop.org/article/10.1088/1402-4896/ac9dc6/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084275852","display_name":"Muhammad Ahsan","orcid":"https://orcid.org/0000-0001-5203-4577","observed_orcids":["https://orcid.org/0000-0001-5203-4577"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210142599","display_name":"University of Swabi","ror":"https://ror.org/04ez8az68","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210142599"]}],"countries":["CN","PK"],"is_corresponding":false,"raw_author_name":"Muhammad Ahsan","raw_affiliation_strings":["Department of Mathematics, University of Swabi, Pakistan","School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0001-5203-4577","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Swabi, Pakistan","institution_ids":["https://openalex.org/I4210142599"]},{"raw_affiliation_string":"School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075863898","display_name":"Weidong Lei","orcid":"https://orcid.org/0000-0002-8022-7074","observed_orcids":["https://orcid.org/0000-0002-8022-7074"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weidong Lei","raw_affiliation_strings":["School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, People's Republic of China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Masood Ahmad","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Masood Ahmad","raw_affiliation_strings":["Department of Basic Sciences, University of Engineering and Technology Peshawar, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, University of Engineering and Technology Peshawar, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045301912","display_name":"Mohammed Sabah Hussein","orcid":"https://orcid.org/0000-0002-9456-4303","observed_orcids":["https://orcid.org/0000-0002-9456-4303"]},"institutions":[{"id":"https://openalex.org/I135120706","display_name":"University of Baghdad","ror":"https://ror.org/007f1da21","country_code":"IQ","type":"education","lineage":["https://openalex.org/I135120706"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"M S Hussein","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq","institution_ids":["https://openalex.org/I135120706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084666686","display_name":"Zaheer Uddin","orcid":"https://orcid.org/0000-0002-1310-3813","observed_orcids":["https://orcid.org/0000-0002-1310-3813"]},"institutions":[{"id":"https://openalex.org/I4210112203","display_name":"CECOS University","ror":"https://ror.org/01xyxtp53","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210112203"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Zaheer Uddin","raw_affiliation_strings":["Department of Basic Sciences, CECOS University of IT and Emerging Sciences Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-1310-3813","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, CECOS University of IT and Emerging Sciences Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I4210112203"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5084666686"],"corresponding_institution_ids":["https://openalex.org/I4210112203"],"apc_list":{"value":2115,"currency":"USD","value_usd":2115},"apc_paid":null,"fwci":4.6398,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.96985129,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"97","issue":"12","first_page":"125208","last_page":"125208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0052999998442828655,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13116","display_name":"Heat Transfer and Numerical Methods","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse-heat-conduction-problem","display_name":"inverse heat conduction problem","score":0.9890000224113464},{"id":"https://openalex.org/keywords/haar-wavelet-collocation-method","display_name":"Haar wavelet collocation method","score":0.8880000114440918},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.8849999904632568},{"id":"https://openalex.org/keywords/linear-parabolic-equations","display_name":"linear parabolic equations","score":0.8629999756813049},{"id":"https://openalex.org/keywords/numerical-stability-and-convergence","display_name":"numerical stability and convergence","score":0.7170000076293945}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6285200715065002},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6254521608352661},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6139367818832397},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.5846890211105347},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5798616409301758},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.519719123840332},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.5193027853965759},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.46109190583229065},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.4606630206108093},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45127928256988525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45098716020584106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2465209662914276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19669991731643677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07260635495185852},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1088/1402-4896/ac9dc6","doi":"https://doi.org/10.1088/1402-4896/ac9dc6","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1402-4896/ac9dc6","pdf_url":"https://iopscience.iop.org/article/10.1088/1402-4896/ac9dc6/pdf","source":{"id":"https://openalex.org/S59012888","display_name":"Physica Scripta","issn_l":"0031-8949","issn":["0031-8949","1402-4896"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physica Scripta","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1088/1402-4896/ac9dc6","doi":"https://doi.org/10.1088/1402-4896/ac9dc6","is_oa":true,"landing_page_url":"https://doi.org/10.1088/1402-4896/ac9dc6","pdf_url":"https://iopscience.iop.org/article/10.1088/1402-4896/ac9dc6/pdf","source":{"id":"https://openalex.org/S59012888","display_name":"Physica Scripta","issn_l":"0031-8949","issn":["0031-8949","1402-4896"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-40","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physica Scripta","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4307407384.pdf","grobid_xml":"https://content.openalex.org/works/W4307407384.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W271203032","https://openalex.org/W1837352056","https://openalex.org/W1968027003","https://openalex.org/W1980133258","https://openalex.org/W1981684771","https://openalex.org/W1983543743","https://openalex.org/W2006264422","https://openalex.org/W2014896403","https://openalex.org/W2019799889","https://openalex.org/W2035176821","https://openalex.org/W2037793948","https://openalex.org/W2042427812","https://openalex.org/W2042819463","https://openalex.org/W2044231677","https://openalex.org/W2050462387","https://openalex.org/W2060722947","https://openalex.org/W2062485267","https://openalex.org/W2065324458","https://openalex.org/W2086043021","https://openalex.org/W2092254180","https://openalex.org/W2094960712","https://openalex.org/W2165281880","https://openalex.org/W2238131983","https://openalex.org/W2287237519","https://openalex.org/W2319615038","https://openalex.org/W2473821723","https://openalex.org/W2562805810","https://openalex.org/W2624793077","https://openalex.org/W2772987450","https://openalex.org/W2788929455","https://openalex.org/W2791447652","https://openalex.org/W2809146903","https://openalex.org/W2811461037","https://openalex.org/W2910796724","https://openalex.org/W2921799630","https://openalex.org/W2945230515","https://openalex.org/W2997023604","https://openalex.org/W3128664950","https://openalex.org/W3207035402","https://openalex.org/W3216412618","https://openalex.org/W3217165160","https://openalex.org/W4210364889","https://openalex.org/W4241513753","https://openalex.org/W4244063180","https://openalex.org/W4290793773","https://openalex.org/W4292133435","https://openalex.org/W4296960860"],"related_works":["https://openalex.org/W2791447652","https://openalex.org/W4296960860","https://openalex.org/W3216412618","https://openalex.org/W2809146903","https://openalex.org/W2922605633","https://openalex.org/W4408556972","https://openalex.org/W2130744364","https://openalex.org/W3023076899","https://openalex.org/W1985801356","https://openalex.org/W2894636083"],"abstract_inverted_index":{"Abstract":[0],"This":[1,82],"paper":[2],"is":[3,47,84,119],"devoted":[4],"to":[5,36,60,92,98,128,142],"an":[6,41],"inverse":[7,38,94],"problem":[8],"of":[9,53,113,146,152],"determining":[10],"discontinuous":[11,64],"space-wise":[12,43,65],"dependent":[13,44,66],"heat":[14,45,67],"source":[15,46,68,154],"in":[16,102],"a":[17,32,110],"linear":[18],"parabolic":[19],"equation":[20],"from":[21],"the":[22,25,29,37,62,71,79,93,124,129,144,147,153],"measurements":[23],"at":[24],"final":[26],"moment.":[27],"In":[28,96],"existing":[30],"literature,":[31],"considerably":[33],"accurate":[34],"solution":[35,126,131],"problems":[39],"with":[40],"unknown":[42,63],"impossible":[48],"without":[49,77,132],"introducing":[50],"any":[51,134],"type":[52],"regularization":[54,80],"method":[55,75,118],"but":[56],"here":[57],"we":[58,104],"have":[59],"determine":[61],"accurately":[69],"using":[70],"Haar":[72,89,106],"wavelet":[73],"collocation":[74],"(HWCM)":[76],"applying":[78],"technique.":[81],"HWCM":[83,148],"based":[85],"on":[86],"finite-difference":[87],"and":[88,121],"wavelets":[90],"approximation":[91],"problem.":[95],"contrast":[97],"other":[99],"numerical":[100,125,138],"techniques,":[101],"HWCM,":[103],"used":[105],"functions":[107],"that":[108],"create":[109],"well-conditioned":[111],"system":[112],"algebraic":[114],"equations.":[115],"The":[116],"proposed":[117],"stable":[120],"convergent":[122],"because":[123],"converges":[127],"exact":[130],"observing":[133],"difficulty.":[135],"Finally,":[136],"some":[137],"examples":[139],"are":[140],"presented":[141],"verify":[143],"validity":[145],"for":[149],"different":[150],"cases":[151],"term.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":6}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2022-11-01T00:00:00"}
